Answer:
A. 0.31
B. Probability of a hurricane decreases. (0.69 to 0.4709)
Probability of a storm increases. (0.31 to 0.5290)
C. Decreased from 0.69 to 0.4709
Step-by-step explanation:
A. The probability Isaac becomes a hurricane is 0.69
The probability of it NOT becoming a hurricane would then be: 1 - 0.69
This is 0.31, which is the answer
B. Let's first take out the probabilities of a hurricane passing over Cuba, and a storm passing over Cuba. These are:
Hurricane passing over Cuba: 0.69 * 0.08 = 0.0552
Tropical Storm passing over Cuba: 0.31 * 0.2 = 0.062
Since it is already given that the hurricane / tropical storm is passing over Cuba, the only probabilities we need to consider are the one's we just calculated above.
Total probability : 0.0552 + 0.062 = 0.1172
New probability of hurricane, given it passes over Cuba: ![\frac{0.0552}{0.1172} = 0.4709](https://tex.z-dn.net/?f=%5Cfrac%7B0.0552%7D%7B0.1172%7D%20%3D%20%200.4709)
New probability of storm, given it passes over Cuba: ![\frac{0.062}{0.1172} = 0.5290](https://tex.z-dn.net/?f=%5Cfrac%7B0.062%7D%7B0.1172%7D%20%3D%20%200.5290)
C. Initial probability of storm becoming a hurricane: 0.69
Probability of storm becoming a hurricane, given it passes over Cuba: 0.4709
Thus we can see the probability decreases from 0.69 to 0.4709.